Apparent frequency when source of moving towards observer, $f_1=100=f_0\left(\frac{c}{c-v_s}\right) ...\left(1\right)$

Here, $f_0=$frequency of observer, $c=$speed of sound and $v_s=$ speed of source.

Apparent frequency when source of moving away from observer, 

$f_2=50=f_0\left(\frac{c}{c+v_s}\right) ...\left(2\right)$

From above two equations, we have 

$\frac{f_1}{f_2}=2=\frac{c+v_s}{c-v_s}$

$\Rightarrow 2c-2v_s=c+v_s$

$\Rightarrow 3v_s=c$

Putting the value in equation $\left(1\right)$, we have

$100=f_0\frac{c}{{\displaystyle \frac{2c}{3}}}=\frac{3}{2}{f}_0$

$\Rightarrow f_0=\frac{200}{3} \mathrm{Hz}$

Hence, $x=200$.